부산대학교 도서관

Quantile Regression, proposed by Koenker and Bassett(1978), provides comprehensive information on the relationship between response and explanatory variables by estimating the conditional quantile function for the response variables. Hence, QR has been used in many fields based on the robustness and usefulness of estimation. The selection of significant explanatory variables when fitting the quantile regression model is an important problem, and research on the shrinkage estimation using penalty function has been actively conducted. Representative penalty function is LASSO, adaptive LASSO, SCAD, and MCP. At this time, LASSO has the advantage of being simple, but there is a disadvantage in that there is a Bias in estimating non-zero regression coefficients. To overcome the disadvantage of LASSO, nonconvex penalty functions SCAD and MCP have been proposed, and many studies have confirmed that nonconvex penalty function-based quantile regression models have Oracle properties. However, when the sample size is small or the signal strength of the actual underlying model is small, the predictive accuracy of the nonconvex penalty function-based regression model is often inferior to LASSO for finite samples. In this paper, we propose a model that applies the Moderately Clipped LASSO(MCL) penalty function, proposed by Kwon, Lee, and Kim(2014), to quantile regression to overcome the disadvantages of LASSO and nonconvex penalty function as above. MCL is known to exhibit high prediction accuracy, successfully select important variables, and preserve the advantages of LASSO and MCP. In addition, MCL is asymptotically identical to Oracle estimator under some regularity conditions. In numerical study, the performance of the MCL quantile regression model proposed in this paper was compared with the existing major nonconvex penalized quantile regression model. At this time, Iterative Coordinate Descent(QICD) Algorithm was used as the optimization algorithm. The suitability of the model was compared based on Bayesian Information Criteria (BIC) and for high-dimensional data, it was compared based on the high-dimensional Bayesian Information Criteria (HBIC). The predictive performance of the model was compared based on the Quantile Loss function and the Mean Absolute Error (MAE). The simulation considered two scenarios, and , based on the magnitude relationship between the explanatory variable and number of data. As a result, the performance of the MCL quantile regression model in the scenario of high-dimensional data were superior to the existing nonconvex penalized quantile regression model. Next, as a result of performing an empirical analysis through high-dimensional real estate data, it was confirmed that the difference in predictive accuracy and model suitability of the MCL quantile regression model varies depending on the quantile . However, in most cases, the performance of the MCL quantile regression model was superior to that of other regression models. Therefore it is expected that future research will lead to the development of the performance of Moderately Clipped LASSO qauntile regression model.